Unit 4
Polynomials
Standard
19a
19b
20
21a
21b
22
Topic
Use properties of exponents
Rewrite radical & rational exponents
Add & subtract polynomials
Multiply polynomials
Solve polynomial area problems
Factor quadratics
4.1 Properties of Exponents
Practice
Simplify:
1. !! !! !!
2. ! ! ! !" !
3. !! ! ! !! ! !
4. 4!! ! 3! ! ! !
5. −5!! 3!!
6. 10!
8. 3!! !
9. 2! ! ! !
7. −6!
!
!
!
!
Find the area of the figure. Express the answer as a monomial.
10.
11.
!!
12. !!
15.
18.
13.
!! ! !
!
!! !
!!"! ! !!!
!!!
!! !"
!! ! ! !
14. !! ! ! !
!! !
16. p(!!! )(!! !! )
19.
! !! ! !
! !!
!
17.
! !!
!
!! !! !! ! !
20. !"!!! !!! !!
!!
21. (!!)!
24.
22.
! !! ! !
!!
!!! !!!
!! !! !!
25.
!! !
23.
!! !! ! !
(!! !! !)!!
!! ! ! !
!!
! ! !! !!
Write each expression in radical form, or write each radical in exponential form.
26. 37
27. 7!"
!
!
!
!
28. 21! !
29. 13(!")!
Simplify
!
30.
! !
!"
31.
!
1024
32.
!"
!"#$
!
!
!
33. 3125!
Review Problems (complete all)
34. Solve for y: 3! − 5! = −12
35. Write the algebraic statement to model
the inequality.
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36. An art collection is valued at $50,000 in 2001 (year 1) and It’s value increased
by $4000 annually. Write an equation using arithmetic sequence to represent
this situation.
>
37. Solve for y and graph
2! − 3! = −16
38. Solve for x:
!
−!! = 2
39. If the first Now=-9, which equation represent this sequence?
-9, -4, 1, 6, 11, …
(a) Next=Now – 5 (b) Next = Now + 5 (c) Next = 5∙Now-1 (d) Next=5∙Now-1
40. The graph of y=3x-1 is shown. If the slope of the
line is doubled, the new equation is y=6x-1. Which of
these is a correct comparison of the two lines?
(a) The x-intercept & y-intercept change
(b) The x-intercept & y- intercept stay the same
(c) The x-intercept changes, and the y-intercept is the
same.
(d) The x-intercept is the same, and the y-intercept
changes.
4.2 Add & Subtract Polynomials
Practice
1. (2x + 3y) + (4x + 9y)
2. (6s + 5t) + (4t + 8s)
3. (5a + 9b) – (2a + 4b)
4. (11m – 7n) – (2m + 6n)
5. (!! – m) + (2m + !! )
6. (! ! – 3x) – (2! ! + 5x)
7. (! ! – d + 5) – (2d + 5)
8. (2ℎ! – 5h) + (7h – 3ℎ! )
9. (5f + g – 2) + (–2f + 3)
10. (6! ! + 2k + 9) + (4! ! – 5k)
11. (10! ! + 5c + 10) + (-2! ! – 5c)
12. (6p4+ 2p3) + (8p3- 5p - 3p4)
13. (3g4+ 2g3+ 9) + (8g3- 4g2- 7)
4k)
14. (7k + 5k4) + (9k + 8k3) + (3k3 + 2k4+
15. (4n3 + 8n2 - 9) + (5n2 + 3) - (7n3 + 2n)
16. Find the perimeter of the rectangle.
17. The perimeter of the pentagon is 7x4+9x3-6x2+10, what
is the missing side?
18. If the perimeter of a square is 12x5-8x2+20x-4, what is the length of one side?
19. Ana knows the perimeter of her backyard is (6x2+14x) feet. If the length of
her backyard is (2x2+3x-7) feet, what is the width of her backyard?
20. The area of the square is represented by the expression 4x2+4x+1.
The area of the rectangle inside is represented by the expression
x2-5x+6. Using the diagram, find the area of the shaded region.
Review Problems (complete all)
21. Explain the steps to solve −4! + 5 = 2! − 6
22. The sum of three consecutive integers is 249, what are the integers?
23. −3 2! + 5 − 5 < 7! − 1
24. Write an equation to determine the nth
term.
-87, -77, -76, …
25. Write the equation of the line represented in the
graph.
26. Solve the system of equations
4! − ! = 10
2! = 12 − 3!
27. Graph both lines and determine which one is the best line of fit.
a. ! = 10! + 20
b. y=40x
28. A line is represented by the equation -2x + 5y = 20. What is another way to
represent the same line?
29. Write the equation of the line represented in the table.
x
y
-2
10
0
17
4
31
6
38
30. The Robertson family makes a trip to Sonic. They buy three large slushes and
a master blast for a total of $11.89. The price of the master blast is one dollar less
than three times the price of a slush. What is the price of each item? (Round to
two decimal places)
4.3 Multiply Polynomials
Practice
1. 2h(-7h2-4h)
2. 6pq(3p2+4q)
3. -3rt(-2t2+3r)
4. 6x(2x-3)-5(2x2+9x-3)
5. 5w(-7w+3) + 2w(-2w2+19w + 2)
6. (3a-b)(2a-b)
7. (m+5)(m2+4m-8)
8. (3d+3)(2d2+5d-2)
9. (3n2+2n-1)(2n2+n+9)
Solve:
10. 4(8n+3)-5=2(6n+8)+1
Write an expression to represent the area of each figure.
11.
12.
Review Problems (complete all)
13. Solve the system of inequalities by graphing
4! + 2! > 6
−3! − 9! > 12
14. Write the equation of the line that passes through the points (-5, 5) and (0, 3)
15. On the 2nd day of tutoring, Dan got 6 questions correct. By the 12th day of tutoring
he got 17 questions correct. Write a linear model to represent the number of
questions Dan answers each day.
16. Solve the compound inequality: −2! + 5 > 12 or 3 ! − 5 < −6
17. −5 ! + 1 + 3 = −7! − 3
18. Express the equation 5! − ! = 12 in
function form.
19. Use the graphing calculator to calculate the linear
regression equation and correlation coefficient.
Temp (°C)
20
24
36
32
28
38
34
26
What does the slope mean in context of this
problem?
Number of
People in
the Park
280
360
450
420
400
500
475
320
What does the y-intercept mean in context of this problem?
Describe the correlation coefficient.
Does this data set indicate causation? Explain why.
20. (3n2 – 4n + 1) – (8n2 – 4n + 17)
21.
!! ! ! !!
!! !! ! !
!
22. 5xy
!
!
23.
4! + 3! = −1
5! + 4! = 1
23. Athena had 5 times as many quarters as dimes. If the total value of her coins was
$16.20, how many of each kind of coin did she have?